5v^2=6-31v

Solution for 5v^2=6-31v equation:

5v^2=6-31v

We move all terms to the left:

5v^2-(6-31v)=0

We add all the numbers together, and all the variables

5v^2-(-31v+6)=0

We get rid of parentheses

5v^2+31v-6=0

a = 5; b = 31; c = -6;
Δ = b2-4ac
Δ = 312-4·5·(-6)
Δ = 1081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{1081}}{2*5}=\frac{-31-\sqrt{1081}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1081}}{2*5}=\frac{-31+\sqrt{1081}}{10}
$